My x220 has a similar problem. It looks like the two parts are glued together in just a few points so there are tiny gaps. The corners of the lid suffer the most and are very squeaky. I tried taping the corners and then it was all good, except it looked ugly. Is there a way to fix this? Squeaking is very annoying.

if it just squeaking they probably wouldn't attempt to fix it. But if has an ill fitted frame, then they would probably oblige to fix it.

I mean if you are adamant to try melting the plastic as a way to fix this issue, then you could but i would imagine you won't get much success (and my friend also tried it once on a T43 and the result was probably not one would expect, it softened the plastic but it didn't melt it enough to make it stick to the magnesium frame).

If you are going to use a heat gun on the X220 you would probably cause the LCD polarising film to melt.